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Voting, Part II

In the first part of this exercise you collected votes for your questions. Today you have to figure out what they mean.

First Past the Post

For this one, count up the votes.

Whatever say the greatest number of votes, wins.

Suppose you were picking a chocolate bar for your school canteen.

There were 25 votes cast.

If the top vote getter was Oh Henry with 8 votes, then the only chocolate bar your canteen would have would be Oh Henry.

That's a bit of a strange system, isn't it?

Proportional Representation

Count up the votes each item received.

Find out the percentage of votes each item has of the total.

If, for example, an Oh Henry bar gets 17% of the vote, 17% of your canteen's order will be Oh Henrys.

If Twix got 22%, then 22% of your order will be for Twix.

You get the idea, right?

This is an interesting system, but how many different chocolate bars can your canteen handle? Because you can only order so many, figure out which are your top five.

Single Transferable Vote

Okay, this one is a bit difficult. Once again, we're counting up votes to pick the top five items (chocolate bars).

Calculate quota. The quota is the number of items we'll have (5 chocolate bars) plus one, for a total of six.

Find out the total number of votes cast. Divide that total by your quota (six).

Count up the number of first place votes each item receives.

If any item has more than the the total votes needed, then it is declared “played,” elected, or chosen

Distribute surplus votes of played items. So, if an item (chocolate in my case) got nine votes and the quota is six, you would distribute three ballots.

Doing this in a class, we'll just select the most recent ballots to be considered surplus. If you were going to do this in a real election there's a procedure to choose the particular ballots

To distribute surpluses, you look at second preferences.

If there are no more items left that have achieved enough votes to be elected and yet you have to choose more, you drop the one with the lowest vote and distribute its ballots to the next available item (chocolate bar).

Eliminated items (bars) that are already “played” can’t receive more ballots, so you go down to the next valid preference.

If at any point, ballots run out of preferences, they are set aside as exhausted.

If at any point an item meets the needed vote total, we stop and declare it played and distribute surplus votes.

Keep dropping items and distributing later preferences until you are only left with the number you want or you have played the required number.

So what does it all mean?

Good question. What does it all mean? To help figure it out, answer the following questions.

With First Past the Post, who was your winner? (1)

In this system, does everybody's vote "count" or do some people not really help choose the winner?

With Proportional Representation who were your top five? (1)

Since only five items are chosen in Proportional Representation, does everyone's vote "count" or do some people not really help choose the winner?

With Single Transferable Vote, who were your top five? (1)

Were they the same five as with Proportional Representation?

With this system, does everybody's vote "count"?

When might you use each of the three systems? What are the best occasions for this? Explain. (3)